相关论文: Production matrices and Riordan arrays

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

Farey sequences, Stern-Brocot sequences, the Calkin-Wilf sequences are shown to be generated via almost identical second order recurrence relations. These sequences have combinatorial, computational, and geometric applications, and are…

We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

Patterns embody repeating phenomena, and, as such, they are partly but not fully detachable from their context. 'Design patterns' and 'pattern languages' are established methods for working with patterns. They have been applied in…

In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…

Let $A$ be a proper Riordan array with general element $a_{n,k}$. We study the one parameter family of matrices whose general elements are given by $a_{2n+r, n+k+r}$. We show that each such matrix can be factored into a product of a Riordan…

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can…

Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…

The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by…

We describe an approach to modelling and reasoning about data-centric business processes and present a form of general model checking. Our technique extends existing approaches, which explore systems only from concrete initial states.…

Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…

We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…

We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…

These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…

A redundant generating function is a generating function having terms which are not part of the solution of the original problem. We use redundant generating functions to study two path problems. In the first application we explain a…